scholarly journals On Characterization of Optimal Control Model of Whooping Cough

2021 ◽  
pp. 175-188
Author(s):  
A. S. Ismail ◽  
Y. O. Aderinto
Keyword(s):  
Optimal Control ◽  
Whooping Cough ◽  
Equilibrium Points ◽  
Public Health Problem ◽  
Sweep Method ◽  
Optimal Control Strategy ◽  
Runge Kutta Method ◽  
Disease Free ◽  
Forward Backward Sweep Method

Whooping cough is a vaccine avoidable public health problem which is caused by bacterium Bordetella Pertussis and it is a highly contagious disease of the respiratory system. In this paper, an SIR epidemiological model of whooping cough with optimal control strategy was formulated to control the transmission. The model was characterized to obtain the disease free and the endemic equilibrium points. Finally, the simulation was carried out using the Forward-backward sweep method by incorporating the Runge Kutta method to check the validity and the result obtained was an improvement over the existing results.

scholarly journals A Discrete Mathematical Modeling and Optimal Control of the Rumor Propagation in Online Social Network

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Amine El Bhih ◽  
Rachid Ghazzali ◽  
Soukaina Ben Rhila ◽  
Mostafa Rachik ◽  
Adil El Alami Laaroussi
Keyword(s):  
Optimal Control ◽  
Online Social Network ◽  
Discrete Version ◽  
Optimal Controls ◽  
Optimal Control Strategy ◽  
Rumor Spreading ◽  
Rumor Propagation ◽  
Theoretical Results ◽  
Forward Backward Sweep Method

In this paper, a new rumor spreading model in social networks has been investigated. We propose a new version primarily based on the cholera model in order to take into account the expert pages specialized in the dissemination of rumors from an existing IRCSS model. In the second part, we recommend an optimal control strategy to fight against the spread of the rumor, and the study aims at characterizing the three optimal controls which minimize the number of spreader users, fake pages, and corresponding costs; theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle. To illustrate the theoretical results obtained, we propose numerical simulations for several scenarios applying the forward-backward sweep method (FBSM) to solve our optimality system in an iterative process.

scholarly journals Mathematical Modeling of Transmission Dynamics and Optimal Control of Vaccination and Treatment for Hepatitis B Virus

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Ali Vahidian Kamyad ◽  
Reza Akbari ◽  
Ali Akbar Heydari ◽  
Aghileh Heydari
Keyword(s):  
Optimal Control ◽  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Public Health Problem ◽  
Hbv Infection ◽  
Optimal Control Strategy ◽  
B Virus ◽  
Existence And Stability ◽  
Steady State Solutions ◽  
Disease Free

Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study the dynamics of hepatitis B virus (HBV) infection which can be controlled by vaccination as well as treatment. Initially we consider constant controls for both vaccination and treatment. In the constant controls case, by determining the basic reproduction number, we study the existence and stability of the disease-free and endemic steady-state solutions of the model. Next, we take the controls as time and formulate the appropriate optimal control problem and obtain the optimal control strategy to minimize both the number of infectious humans and the associated costs. Finally at the end numerical simulation results show that optimal combination of vaccination and treatment is the most effective way to control hepatitis B virus infection.

scholarly journals Optimal Control of an HIV Model with Gene Therapy and Latency Reversing Agents

2021 ◽  
Vol 26 (4) ◽  
pp. 77
Author(s):  
Zachary Abernathy ◽  
Kristen Abernathy ◽  
Andrew Grant ◽  
Paul Hazelton
Keyword(s):  
Gene Therapy ◽  
Optimal Control ◽  
Combination Treatment ◽  
Latent Reservoir ◽  
Sweep Method ◽  
Hiv Model ◽  
Future Work ◽  
Disease Free ◽  
Forward Backward Sweep Method ◽  
Reversing Agents

In this paper, we study the dynamics of HIV under gene therapy and latency reversing agents. While previous works modeled either the use of gene therapy or latency reversing agents, we consider the effects of a combination treatment strategy. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of R0. We then consider time-dependent controls and formulate an associated optimal control problem that emphasizes reduction of the latent reservoir. Characterizations for the optimal control profiles are found using Pontryagin’s Maximum Principle. We perform numerical simulations of the optimal control model using the fourth-order Runge–Kutta forward-backward sweep method. We find that a combination treatment of gene therapy with latency reversing agents provides better remission times than gene therapy alone. We conclude with a discussion of our findings and future work.

scholarly journals Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network

2021 ◽  
Vol 19 (2) ◽  
pp. 1677-1695
Author(s):  
Boli Xie ◽  
◽  
Maoxing Liu ◽  
Lei Zhang
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Virus Transmission ◽  
Population Heterogeneity ◽  
Multiple Equilibrium ◽  
Optimal Control Strategy ◽  
Treatment Function ◽  
The Stability ◽  
The Impact

<abstract><p>In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} &lt; 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.</p></abstract>

OPTIMAL CONTROL FOR A NONLINEAR n-DIMENSIONAL COMPETING SYSTEM WITH AGE-STRUCTURE

2012 ◽  
Vol 05 (03) ◽  
pp. 1260008 ◽  
Author(s):  
ZHI-XUE LUO ◽  
JIAN-YU YANG ◽  
YA-JUAN LUO
Keyword(s):  
Optimal Control ◽  
Age Structure ◽  
Normal Cone ◽  
Equation System ◽  
Optimal Harvesting ◽  
Order Partial Differential Equation ◽  
Differential Equation System ◽  
Optimal Control Strategy ◽  
First Order

This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland's variational principle, the existence and unique characterization of the optimal control strategy are established. The optimality conditions for the control problem are obtained by the concept of the normal cone.

scholarly journals Implementation and acceleration of optimal control for systems biology

2021 ◽  
Vol 18 (181) ◽  
pp. 20210241
Author(s):  
Jesse A. Sharp ◽  
Kevin Burrage ◽  
Matthew J. Simpson
Keyword(s):  
Optimal Control ◽  
Systems Biology ◽  
Iteration Process ◽  
System Size ◽  
Sweep Method ◽  
Acceleration Techniques ◽  
Fixed Point Iteration Process ◽  
Allocation Decisions ◽  
Insight Into ◽  
Forward Backward Sweep Method

Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021 .

scholarly journals Mathematical Modeling and Optimal Control Analysis of COVID-19 in Ethiopia

2020 ◽  
Author(s):  
Haileyesus Tessema Alemneh ◽  
Getachew Teshome Telahun
Keyword(s):  
Optimal Control ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Control Model ◽  
Control Analysis ◽  
Basic Model ◽  
Short Period ◽  
Disease Free

In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagins Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.

scholarly journals Application of Optimal Control to Influenza Pneumonia Coinfection with Antiviral Resistance

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Caroline W. Kanyiri ◽  
Livingstone Luboobi ◽  
Mark Kimathi
Keyword(s):  
Optimal Control ◽  
Optimal Strategies ◽  
Antiviral Resistance ◽  
System Control ◽  
High Morbidity ◽  
Prevention Measures ◽  
Sweep Method ◽  
Influenza Pneumonia ◽  
Major Impediment ◽  
Forward Backward Sweep Method

Influenza and pneumonia independently lead to high morbidity and mortality annually among the human population globally; however, a glaring fact is that influenza pneumonia coinfection is more vicious and it is a threat to public health. Emergence of antiviral resistance is a major impediment in the control of the coinfection. In this paper, a deterministic mathematical model illustrating the transmission dynamics of influenza pneumonia coinfection is formulated having incorporated antiviral resistance. Optimal control theory is then applied to investigate optimal strategies for controlling the coinfection using prevalence reduction and treatment as the system control variables. Pontryagin’s maximum principle is used to characterize the optimal control. The derived optimality system is solved numerically using the Runge–Kutta-based forward-backward sweep method. Simulation results reveal that implementation of prevention measures is sufficient to eradicate influenza pneumonia coinfection from a given population. The prevention measures could be social distancing, vaccination, curbing mutation and reassortment, and curbing interspecies movement of the influenza virus.

scholarly journals Optimal Control of Mathematical Models on The Dynamics Spread of Drug Abuse

2021 ◽  
Vol 17 (3) ◽  
pp. 339-348
Author(s):  
Nita Anggriani ◽  
Syamsuddin Toaha ◽  
Kasbawati Kasbawati
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Drug Abuse ◽  
Mathematical Models ◽  
Minimum Principle ◽  
Self Psychology ◽  
Sweep Method ◽  
Pontryagin Minimum Principle ◽  
Counseling Needs ◽  
Forward Backward Sweep Method

This article examines the optimal control of a mathematical model of the spread of drug abuse. This model consists of five population classes, namely susceptible to using drugs (S), light-grade drugs (A), heavy-grade drugs (H), medicated drugs (T), and Recovery from drugs (R). The system is solved using the Pontryagin minimum principle and numerically by the forward-backward sweep method. Numerical simulations of the optimal problem show that with the implementation of anti-drug campaigns and strengthening of self-psychology through counseling, the spread of drug abuse can be eradicated more quickly. The implementation of campaigns and strengthening of self-psychology through large amounts of counseling needs to be done from the beginning then the proportion can be reduced until a certain time does not need to be given anymore. The use of control in the form of strengthening efforts to self-psychology through counseling means that it needs to be done in a longer time to prevent the spread of drug abuse.

Sign in / Sign up

Export Citation Format

Share Document